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Hyperbolic volume potential functions and knotted graph complements : 쌍곡 부피 잠재함수와 매듭진 그래프 여공간

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dc.contributor.advisor김 혁-
dc.contributor.author김선화-
dc.date.accessioned2017-07-14T00:40:35Z-
dc.date.available2017-07-14T00:40:35Z-
dc.date.issued2013-08-
dc.identifier.other000000013965-
dc.identifier.urihttps://hdl.handle.net/10371/121273-
dc.description학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2013. 8. 김혁.-
dc.description.abstract양자불변량의 낙관적 극한법은 카샤에브 부피가설을 풀려는 시도로 개발되었다. 비록 수학적으로 엄밀하게 정식화 하긴 매우 힘들어 보이지만, 이 방법을 통해 쌍곡 매듭의 부피공식을 명시적으로 쓸 수 있으며 쌍곡부피는 매듭다이어그램으로 부터 직접적으로 쓸수있는 잠재함수의 임계값으로 주어지게 된다. 이 논문에서는 어떤 특정한 형태의 함수의 임계값이 PSL(2,C)-표현의 쌍곡부피가 될 충분조건을 연구하고 매듭진 그래프의 확장된 팔면체 분할을 통해 매듭진 그래프 여공간의 쌍곡 부피를
구하는 잠재함수를 정의한다.
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dc.description.abstractOptimistic limit method of quantum invariants has been developed from an attempt to solve the Kashaev volume conjecture. Although it may seem to be hard to formulate in a rigorous way, this method produces explicit correct volume formulas of hyperbolic links, which are given by the critical values of the potential functions written directly from the link diagrams. In this dissertation, we study a sufficient
condition to produce hyperbolic volumes of PSL(2,C))-representations as critical values of a certain type of functions and also define a volume potential function to
obtain hyperbolic volume of the knotted graph complement considering generalized octahedral decomposition.
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dc.description.tableofcontentsAbstract
Introduction
0 Preliminaries
0.1 Dilogarithm and hyperbolic volume
0.2 Gluing equation and PSL(2,C)-representations
1 Volume Potential function 6
1.1 Volume conjecture
1.2 Optimistic limits
1.3 Potential functions
1.3.1 Volume potential of dilogarithm type
1.3.2 Critical equations
1.3.3 Analytic continuation and compensated evaluation
2 Knotted graph complements
2.1 Hyperbolic structure for complements
2.2 Ideal triangulations
2.2.1 Dual graph decomposition for diagram
2.2.2 Combinatorial features: 1-cell
2.2.3 Combinatorial features: 3-cell
2.3 Edge parametrization
2.3.1 Corner parity system
3 Corner chain complex
3.1 Chain complexes from graphs
3.2 Corner homormorphisms
3.2.1 Corners and the incident maps
3.2.2 C,E, VF and homomorphisms
3.3 Corner sequences
3.3.1 CE- and CVF- chain complex
3.3.2 Medial and cubical graph
3.3.3 Corner sequences and induced graph
3.4 Z 2 -coefficient and corner parity systems
4 Volume potential function for knotted graph
4.1 Volume potential function for knotted graph
4.2 Example for tetrahedron graph
Abstract (in Korean)
Acknowledgement (in Korean)
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dc.formatapplication/pdf-
dc.format.extent10410588 bytes-
dc.format.mediumapplication/pdf-
dc.language.isoen-
dc.publisher서울대학교 대학원-
dc.subjectVolume Conjecture-
dc.subjectQuantum topology-
dc.subjectHyperbolic geometry-
dc.subjectLow dimensional topology-
dc.subjectGraph-
dc.subject.ddc510-
dc.titleHyperbolic volume potential functions and knotted graph complements-
dc.title.alternative쌍곡 부피 잠재함수와 매듭진 그래프 여공간-
dc.typeThesis-
dc.description.degreeDoctor-
dc.citation.pages1,44-
dc.contributor.affiliation자연과학대학 수리과학부-
dc.date.awarded2013-08-
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